We saw in the last chapter that Hempel (1) asserted that a functional ascription is supposed to explain why the function bearer occurs and (2) denied that the explanation is valid. For the purposes of this exposition, I shall count as a “Hempelian” anyone who interprets functional explanation in the sense of the first proposition, whether or not they side with Hempel on the second. This is not to deny that there are significant differences, even in fundamental philosophical assumptions, between Hempel and his followers, differences that from the point of view of Logical Empiricism would even seem crucial. In fact, most of Hempel's successors have not only attempted, against Hempel, to interpret functional explanation as legitimate, they have also abandoned the D-N scheme – at least so far as biology is concerned – and they openly revel in causal considerations. And whereas Hempel and Nagel said almost nothing about evolution in this context, the next generation of philosophers of science has a strong tendency to speak about almost nothing else. A concerted effort has been mounted to rescue functional explanation by means of natural selection, thus often narrowing its scope to biology. Nonetheless, Hempel's analysis has defined the problem and set the agenda for much of the literature of the past 40 years. In this chapter, I shall analyze four positions that represent the spectrum of lines of development of the basic Hempelian position: one dealing strictly with explanation in biology (Ruse); one analysis of functional explanation in social science (Elster); a general analysis of function ascriptions (Wright); and finally a prolegomenon to a naturalist philosophy of mind (Millikan).